Even at night, it was safe Giuliani and Bloomberg. I was there one summer night with a friend, about 11 p.m. Large crowd, all sorts of street performers. One guy had a grand piano! that he played in the park.
Farther south is the Wall Street area. You might want to visit the bull statue, or tour the NY Stock Exchange.
Or go up the Empire State Building.
Both the Empire State Building and Stock Exchange require tickets. You might even have to buy them in advance.
Central Park is worth seeing. Don't go too far north, that's closer to the bad areas. I don't know if they still have horse carriage rides. The PETA people have been trying to shut them down.
Highly recommend you DON’T go to Washington Sq Park- its infested with druggies and has turned into a complete craphole. The area around it is nice.
They do have the handsome cab rides in the Park. Its usually best around the holidays but good anytime of year. Go for the extended ride- not the 30 minute version. Also best to go during the day as you see more.
Central Park is wonderful, but never after dark. Not even in your car while driving through.